Question

a surfboard shaper has to limit the cost of development and production to $260 per surfboard. he has already spent $57,720 on equipment for the boards. the development and production costs are $140 per board. the cost per board is $\frac{140x + 57720}{x}$ dollars. determine the number of boards that must be sold to limit the final cost per board to $260.
how many boards must be sold to limit the cost per board to $260?$

Explanation:

Step1: Set up the cost - per - board equation

Let $x$ be the number of surfboards. The cost - per - board formula is $\frac{140x + 57720}{x}=260$.

Step2: Multiply both sides by $x$

$140x + 57720=260x$ (to get rid of the denominator).

Step3: Rearrange the equation

$57720=260x - 140x$.

Step4: Simplify the right - hand side

$57720 = 120x$.

Step5: Solve for $x$

$x=\frac{57720}{120}=481$.

Answer:

481